Question

What is the quotient of the complex numbers below?A.10 - iB.2 - iC.2 + iD.10 + i

Answer 1

The given fraction is

`(7+i)/(3-i)`

We will multiply up and down by the conjugate of down (3 + i)

`\begin{gathered} (7+i)/(3-i)*(3+i)/(3+i)= \\ \\ ((7+i)(3+i))/((3-i)(3+i))= \\ \\ ((7)(3)+(7)(i)+(i)(3)+(i)(i))/((3)(3)-(i)(i))= \end{gathered}`

Add the like terms

`\begin{gathered} (21+7i+3i+i^2)/(9-i^2)= \\ \\ (21+10i-1)/(9-(-1))= \\ \\ (20+10i)/(9+1)= \\ \\ (20+10i)/(10) \end{gathered}`

Take 10 as a common factor from up

`\begin{gathered} (10(2+i))/(10)= \\ \\ 2+i \end{gathered}`

The answer is C